Find the exact value of sin 5x/6

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ab=9, and ac=12, find hc.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Before simplifying, how many terms are there in the expression 2x - 5y + 3 + x?